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25 December, 23:10

Addison earns a fixed hourly rate working as a sales clerk. If she works on a holiday, she earns a different hourly rate than she earns on a regular day. In one week, she earns $188.50 by working 5 hours on a holiday and 16 hours during regular days. A different week, she earns $254.00 by working 8 hours on a holiday and 20 hours during regular days. How much more is Addison's holiday hourly rate than her regular hourly rate?

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  1. 25 December, 23:17
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    Be r the regular rate and h the hoiday's rate.

    Then you can write this two equations:

    From the first statement:

    188.50 = 5h + 16r

    From the second statement:

    254.00 = 8h + 20r.

    There you have a system of two independent equations with two variables, which you can solve by several methods.

    If you multiply the first by 8 and the second by 5, you get:

    40h + 128r = 1508

    40h + 100r = 1270

    Substract the second equation from the first one:

    28r = 238

    Divide by 28

    r = 238/28 = 8.5

    You can use now any of the two original statements to find h

    254.00 = 8h + 20r

    8h = 254 - 20 (8.5) = 84

    h = 84/8 = 10.5

    Solution:

    h - r = 10.50 - 8.50 = 2.00

    The holiday hourly rate is $2.00 more than the regular hourly rate.
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